He introduced the so-called Zaanen-Sawatzky-Allen diagram, the LDA+U band structure method and he became particularly well known for his discovery of the stripe instability of the doped Mott insulator. His present research is focused on the quantum critical point and unconventional phases of quantum matter. He is a well-known proponent of the application of Holographic principle to condensed matter physics [1]. He is also well known for his many editorial contributions to the journals Nature and Science. He is currently on the board of reviewing editors of the latter journal and also editor of the Journal of High Energy Physics.

After winning the Spinoza Prize, it was no longer necessary to worry whether I was proving myself enough. You start looking at things you really like. Furthermore I wanted to prove that I was not too old to learn new things. String theory really is another ballgame than the rest of physics] and I'm proud that I was able to learn it.

Recently Zaanen is known for his contribution to the understanding of high-temperature superconductivity. In most high-temperature superconductors the copper atoms are arranged in thin layers. Each atom has its own magnetic field which is opposite to that of its neighbor. Electrons can scarcely move in such an environment, as they are also magnetic. Recently, Zaanen and colleagues Cubrovic and Schalm applied String Theory to explain a physical phenomenon.[5] Initially the String Theory attracted a lot of criticism.[6][7][8][9][10][11] However, in recent years an increasing amount of experimental evidence has been collected in its favor. Its latest accomplishment is the development of the AdS/CFT correspondence theory, sometimes called Maldacena duality or gauge/gravity duality.

Once it was realised that AdS/CFT could be applied to a broader spectrum of physical phenomena,[12] Zaanen was inspired to use these ideas for his own area of High-temperature superconductivity. Zaanen stated:

"It has always been assumed that once you understand this quantum-critical state, you can also understand high temperature super-conductivity. But, although the experiments produced a lot of information, we hadn't the faintest idea of how to describe this phenomenon. We hadn't expected it to work so well, the maths was a perfect fit; it was superb. When we saw the calculations, at first we could hardly believe it, but it was right."[13]